Non-equilbrium phases of shaken lithium atoms within the BEC-BCS crossover

Ultracold atoms in temporally periodic optical lattices are out-of-equilibrium systems in multiple senses. Even when they are in quasi-equilibrium Floquet states at the timescale of the driving, the resulting dispersion relation can be rapidly tuned, resulting in out-of-equilibrium momentum distributions. We begin our experiments with a molecular Bose-Einstein condensate (mBEC) in the tightly bound region below a Feshbach resonance. We suddenly change apply the periodic drive to create a double-well momentum distribution, so that the system at zero momentum is in a local maximum of the kinetic energy. The resulting dynamics involves bifurcation of the condensate into two parts, which separately occupy each of the two momentum-space minima. This is a non-adiabatic version of the domain formation seen in bosonic experiments. Counter-diabatic driving can help this system restore equilibrium. As this "split-condensate" settles, we ramp the magnetic field towards the resonance to decrease the binding energy of the pairs. This leads the system out of equilibrium once again. By this method, we hope to prepare exotic phases. For example, the BCS analog of the condensate at two points of momentum space is the FFLO state. The prospects for reaching such phases, and their possible stability under period drive, will be discussed.